自动控制理论(邹伯敏)第3版_第5章答案 khdaw

自动控制理论(邹伯敏)第3版_第5章答案 khdaw
自动控制理论(邹伯敏)第3版_第5章答案 khdaw

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1.242 100%9.45% p d p t s M e π ω === =?= 3 5% 1.581 4 2% 2.108 s n s n t s t s ωζ ωζ ?=≈= ?=≈= 题3-7 解: 0.1 1.31 100%30% 1 p d p t M e π ω === - =?== 上升时间 超调量 =0.3579 33.64 n ζ ω ? ?? = ? 2 2 1131.9 () (2)24.08 n n G s s s s s ω ζω == ++ 开环传递函数 题3-8 (1) 2 100 () (824) G s s s s = ++ 解:闭环传递函数为 2 ()100 ()(824)100 C s R s s s s = +++ 特征方程为32 8241000 s s s +++= 列出劳斯表: 3 2 1240 81000 11.50 100 s s s s 第一列都是正数,所以系统稳定 (2) 10(1) () (1)(5) s G s s s s + = -+

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自动控制原理第六章课后习题答案(免费) 线性定常系统的综合 6-1 已知系统状态方程为: ()100102301010100x x u y x ? -???? ? ?=--+ ? ? ? ?????= 试设计一状态反馈阵使闭环系统极点配置为-1,-2,-3. 解: 由()100102301010100x x u y x ? -???? ? ?=--+ ? ? ? ?????=可得: (1) 加入状态反馈阵()0 12K k k k =,闭环系统特征多项式为: 32002012()det[()](2)(1)(2322)f I A bK k k k k k k λλλλλ=--=++++-+--+- (2) 根据给定的极点值,得期望特征多项式: *32()(1)(2)(3)6116f λλλλλλλ=+++=+++ (3) 比较()f λ与*()f λ各对应项系数,可得:0124,0,8;k k k === 即:()408K =

6-2 有系统: ()2100111,0x x u y x ? -????=+ ? ?-????= (1) 画出模拟结构图。 (2) 若动态性能不能满足要求,可否任意配置极点? (3) 若指定极点为-3,-3,求状态反馈阵。 解(1) 模拟结构图如下: (2) 判断系统的能控性; 0111c U ?? =?? -?? 满秩,系统完全能控,可以任意配置极点。 (3)加入状态反馈阵01(,)K k k =,闭环系统特征多项式为: ()2101()det[()](3)22f I A bK k k k λλλλ=--=+++++ 根据给定的极点值,得期望特征多项式: *2()(3)(3)69f λλλλλ=++=++ 比较()f λ与*()f λ各对应项系数,可解得:011,3k k == 即:[1,3]K =

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(a) (b) (c) (d) (e) (f) 题4-2 解: 由开环传递函数容易得到 3,0n m ==,三个极点分别为1230,42,42p p j p j ==- +=--,因此,有3条根轨迹趋于无穷远,其渐近线倾角为(21)5,, 333 k πππ θπ+= =,渐近线与实轴交点为1 1 ()() 8 3 n m l i l i A p z n m σ==----= =--∑∑。 下面确定根轨迹的分离点和汇合点 2020 12()(0.050.41)00.150.81010 2,3D s s s s K dK s s ds s s =+++=? =---=?=-=- 计算根轨迹的出射角与入射角 2322(arctan())63.4 4 2 63.4 p p p π θππθθ=---=-=-= 确定根轨迹与虚轴的交点

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